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United States Patent |
6,141,452
|
Murao
|
October 31, 2000
|
Apparatus for compressing and restoring image data using wavelet
transform
Abstract
An apparatus for transforming image data using a Wavelet transform,
including an image compressing apparatus having a Wavelet transforming
unit for compressing digitized image data and an image restoring apparatus
having an inverse Wavelet transforming unit for restoring image data
compressed by the image compressing apparatus. The Wavelet transforming
unit in the image compressing apparatus includes a unit for extending
image data area to make the number of data of the object of transform in
horizontal and vertical directions, with every one octave of resolution
lowered when a Wavelet transform is conducted hierarchically based on
multiple resolution analysis, thereby conducting a Wavelet transform on
data of the interpolated image data area. The inverse Wavelet transforming
unit in the image restoring apparatus includes a unit for reducing
redundant portion generated by extension of image data area in the image
data compression, with every one octave of resolution increased. Based on
the above structure, it is possible to minimize zero area to reduce the
computing time and capacity of memory used. It is also possible to
estimate signal-to-noise ratio when data is reduced.
Inventors:
|
Murao; Kohei (Kawasaki, JP)
|
Assignee:
|
Fujitsu Limited (Kawasaki, JP)
|
Appl. No.:
|
825695 |
Filed:
|
March 20, 1997 |
Foreign Application Priority Data
Current U.S. Class: |
382/240; 382/233; 382/250 |
Intern'l Class: |
G06K 009/46 |
Field of Search: |
382/250,244,232,233,235,240
|
References Cited
U.S. Patent Documents
5400154 | Mar., 1995 | Takayama et al. | 358/525.
|
5546477 | Aug., 1996 | Knowles et al. | 382/242.
|
5561464 | Oct., 1996 | Park | 348/397.
|
5602589 | Feb., 1997 | Vishwanath et al. | 348/398.
|
5661822 | Aug., 1997 | Knowles et al. | 382/233.
|
5710835 | Jan., 1998 | Bradley | 382/233.
|
5748786 | May., 1998 | Zandi et al. | 382/240.
|
5841890 | Nov., 1998 | Kraske | 382/131.
|
Primary Examiner: Mehta; Bhavesh
Assistant Examiner: Patel; Kanji
Attorney, Agent or Firm: Staas & Halsey LLP
Claims
What is claimed is:
1. An image compressing apparatus having a Wavelet transforming unit for
compressing digitized image data using a Wavelet transform, said Wavelet
transforming unit comprising:
means for extending image data areas to make the number of data of the
object of transform in horizontal and vertical directions to be the
nearest even number possible, with every one octave of resolution lowered
when a Wavelet transform is conducted hierarchically based on multiple
resolution analysis; and
means for interpolating values in an extended image data area using data in
an image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and the interpolated image data area.
2. The image compressing apparatus as set forth in claim 1, further
comprising:
means for reducing data of smaller amplitude among data transformed by said
Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
3. An image restoring apparatus having an inverse Wavelet transforming unit
restoring image data compressed by a Wavelet transform, said inverse
Wavelet transforming unit comprising means for reducing a redundant
portion, generated by extension of an image data area by adding data
thereto in the image data compression, so that the number of transformed
data, in each of horizontal and vertical directions, coincides with the
number thereof, whether odd or even, before conducting the corresponding
compression, with every one octave of resolution increased.
4. An image compressing apparatus having a Wavelet transforming unit for
compressing digitized image data using a Wavelet transform, said Wavelet
transforming unit comprising:
means for extending an image data area to make the number of data of the
object of transform in horizontal and vertical directions coincide with a
number which can be divided by 2 raised to the power of n (n=a desired
number of hierarchy) in advance, when a Wavelet transform is conducted
hierarchically based on multiple resolution analysis; and
means for interpolating values in an extended image data area using data in
an image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and the interpolated image data area.
5. The image compressing apparatus as set forth in claim 4, further
comprising:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
6. An image restoring apparatus having an inverse Wavelet transforming unit
restoring image data compressed by a Wavelet transform, said inverse
Wavelet transforming unit comprising:
means for reducing a redundant portion, generated by extension of an image
data area by adding data thereto in the image data compression, so that
the number of transformed data, in each of horizontal and vertical
directions, coincides with the original number thereof whether odd or
even, after conducting an inverse Wavelet transform hierarchically.
7. An apparatus for transforming image data using a Wavelet transform,
comprising:
an image compressing apparatus having a Wavelet transforming unit
compressing digitized image data; and
an image restoring apparatus having an inverse Wavelet transforming unit
restoring the image data compressed by said image compressing apparatus,
said Wavelet transforming unit in the image compressing apparatus including
means for extending image data areas to make the number of data of the
object of transform in horizontal and vertical directions to be the
nearest even numbers possible, with every one octave of resolution lowered
when a Wavelet transform is conducted hierarchically based on multiple
resolution analysis, thereby conducting a Wavelet transform on data of the
whole image data area comprised of the original and the interpolated image
data area, and
said inverse Wavelet transforming unit in the image restoring apparatus
including means for reducing a redundant portion generated by extension of
an image data area in the image data compression so that the number of
transformed data in horizontal and vertical directions coincides with the
number before conducting the corresponding compression, with every one
octave of resolution increased.
8. The apparatus as set forth in claim 7, wherein said image compressing
apparatus further comprises:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
9. An apparatus for transforming image data using a Wavelet transform,
comprising:
an image compressing apparatus having a Wavelet transforming unit
compressing digitized image data; and
an image restoring apparatus having an inverse Wavelet transforming unit
restoring image data compressed by said image compressing apparatus;
said Wavelet transforming unit in the image compressing apparatus including
means for extending an image data area to make the number of data of the
object of transform in horizontal and vertical directions coincide with a
number which can be divided by 2 raised to the power of n (n=desired
number of hierarchy) in advance, when a Wavelet transform is conducted
hierarchically based on multiple resolution analysis; and
means for interpolating values in an extended image data area using data in
the image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and interpolated image data area,
said Wavelet transforming unit in the image restoring apparatus including
means for reducing a redundant portion generated by extension of an image
data area in the image data compression so that the number of transformed
data in horizontal and vertical directions coincides with the original
number, after conducting an inverse Wavelet transform hierarchically.
10. The apparatus as set forth in claim 9, wherein the image compressing
apparatus further comprises:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
11. A method of compressing digitized image data using a Wavelet transform,
comprising the steps of:
extending image data areas to make the number of data of the object of
transform in horizontal and vertical directions to be the nearest even
number possible, with every one octave of resolution lowered when a
Wavelet transform is conducted hierarchically based on multiple resolution
analysis; and
interpolating values in an extended image data area using data in an image
data area before being extended, thereby conducting a Wavelet transform on
data of the whole image data area comprised of the original and the
interpolated image data area.
12. An image compressing apparatus having a Wavelet transforming unit for
compressing digitized image data using a Wavelet transform, said Wavelet
transforming unit comprising:
means for extending an image data area by adding data thereto so as to make
the number of data of the object of transform, in each of horizontal and
vertical directions, if odd, to be the next higher number, with every one
octave of resolution lowered when a Wavelet transform is conducted
hierarchically based on multiple resolution analysis; and
means for interpolating values in an extended image data area using data in
an image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and the interpolated image data area.
13. The image compressing apparatus as set forth in claim 12, further
comprising:
means for reducing data of smaller amplitude among data transformed by said
Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
14. An image compressing apparatus having a Wavelet transforming unit for
compressing digitized image data using a Wavelet transform, said Wavelet
transforming unit comprising:
means for extending an image data area by adding data thereto so as to make
the number of data of the object of transform, in each of horizontal and
vertical directions, if odd, coincide with a next higher number which can
be divided by 2 raised to the power of n (n=a desired number of hierarchy)
in advance, when a Wavelet transform is conducted hierarchically based on
multiple resolution analysis; and
means for interpolating values in an extended image data area using data in
an image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and the interpolated image data area.
15. The image compressing apparatus as set forth in claim 13, further
comprising:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
16. An apparatus for transforming image data using a Wavelet transform,
comprising:
an image compressing apparatus having a Wavelet transforming unit
compressing digitized image data; and
an image restoring apparatus having an inverse Wavelet transforming unit
restoring the image data compressed by said image compressing apparatus,
said Wavelet transforming unit in the image compressing apparatus including
means for extending image data areas by adding data thereto so as to make
the number of data of the object of transform, in each of horizontal and
vertical directions, to be the next higher number, with every one octave
of resolution lowered when a Wavelet transform is conducted hierarchically
based on multiple resolution analysis, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and the interpolated image data area, and
said inverse Wavelet transforming unit in the image restoring apparatus
including means for reducing a redundant portion, generated by the
extension of the image data area by adding data thereto in the image data
compression, so that the number of transformed data, in each of horizontal
and vertical directions, coincides with the number thereof, whether odd or
even, before conducting the corresponding compression, with every one
octave of resolution increased.
17. The apparatus as set forth in claim 16, wherein said image compressing
apparatus further comprises:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
18. An apparatus for transforming image data using a Wavelet transform,
comprising:
an image compressing apparatus having a Wavelet transforming unit
compressing digitized image data; and
an image restoring apparatus having an inverse Wavelet transforming unit
restoring image data compressed by said image compressing apparatus;
said Wavelet transforming unit in the image compressing apparatus including
means for extending an image data area by adding data thereto so as to
make the number of data of the object of transform, in each of horizontal
and vertical directions, coincide with a next higher number which can be
divided by 2 raised to the power of n (n=desired number of hierarchy) in
advance, when a Wavelet transform is conducted hierarchically based on
multiple resolution analysis; and
means for interpolating values in an extended image data area using data in
the image data area before being extended, thereby conducting a Wavelet
transform on data of the whole image data area comprised of the original
and interpolated image data area,
said inverse Wavelet transforming unit in the image restoring apparatus
including means for reducing a redundant portion generated by the
extension of the image data area by adding data thereto in the image data
compression, so that the number of transformed data, in of horizontal and
vertical directions, coincides with the original number thereof, whether
odd or even, after conducting an inverse Wavelet transform hierarchically.
19. The apparatus as set forth in claim 18, wherein the image compressing
apparatus further comprises:
means for reducing data having a smaller amplitude among data transformed
by said Wavelet transforming unit; and
means for conducting entropy-coding with respect to said reduced data,
wherein said means for reducing data determines a threshold value of data
to be reduced by quantitatively estimating a quality of the image after
restoration.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an art of transforming image data using a Wavelet
transform, and more particularly to an apparatus for compressing image
which compresses any size of image data using a Wavelet transform as well
as about an apparatus for restoring image which restores the image data
compressed by that image compressing apparatus.
2. Description of the Related Art
In recent years, with growing diffusion of computers and communication
networks, opportunities for collecting, sending and receiving a large
quantity of image data have been increasing. With that reason, the
technology of efficient compressing image data has been demanded.
Images to be subject of this invention include many things from human
figure images, landscape pictures, computer graphics to medical data,
weather data and astronomical observation data.
With image compressing systems like JPEG, the images have been divided into
small block units to be processed by the block unit, assigned zero to the
fractions.
When a Wavelet transform system is used, however, the whole image is
collectively transformed since the computation efficiency will be rather
drooped by dividing into the blocks. In that case, one side length of the
subject image must be only an exponentiation of 2, allowing only using
images with the 64.times.64, 256.times.256 pixels, etc. before.
There are the literature cited for the Wavelet transform as follows;
I. Daubechies "Ten lectures on Wavelets" 1992 SIAM (Society for Industrial
and Applied Mathematics).
W. H. Press et. al "Numeral Recipes (Second Edition)" 1992 Cambridge
University Press pp. 584-599.
FIG. 1a-FIG. 1c describe the compression processing using a Wavelet
transform. To make it simple, the original image size will be described as
8.times.8 pixels (cf. the FIG. 1a) and to x and y directions, 3 octaves of
multiple resolution analysis which will be described later will be
conducted.
In the Wavelet transform, the frequency components will be divided into low
region components and high region components for each horizontal and
vertical directions. With it, the image data will be transformed as
follows; information of low region components of horizontal direction and
low region components of vertical direction in the up left of the image,
information of high region components of horizontal direction and low
region components of vertical direction in the up right, information of
low region components of horizontal direction and high region components
of vertical direction in the down left, information of high region
components of horizontal direction and high region components of vertical
direction in the down right. One transforming makes one octave of the
resolution down.
Then, divide the part of low region components of horizontal direction and
low region components of vertical direction in the up left of the image
into the low region components and high region components of frequency in
the same way. Repeat this several times.
Generally, in the image data, the information is concentrated in the low
region components. Therefore, in the high region components, data
reduction to some extent will not make much deterioration of the image by
restoration. The Wavelet transform, which is a kind of orthogonal
transform like DCT, has a merit that it has relatively less noise
especially when the high region is transformed.
FIG. 1b describes the data after transform processing (multiple resolution
analyzing processing). It shows that the low frequency components and high
frequency components regions are lined up from the left to the right of x
direction and from the up to the down of y direction of the transformed
data, respectively. From this transformed data, it is clear that the
closer the up left low frequency component region, the more the image data
information is concentrated. When the data is reduced, use predetermined
threshold value to make the data which is smaller than the threshold zero.
FIG. 1c shows the data after reduction processing. With it, the high
frequency components region, which has low concentration of the
information, will be efficiently reduced and then the efficient compressed
data can be generated by compressing with encoding entropy, etc.
Restoration processing is conducted by inverse steps of the compression
processing, which is, by decoding entropy and inverse Wavelet transforming
to generate the restored data. FIG. 2 shows the data generated by the
restoration processing.
As described above, when a Wavelet transform was used, one side length of
the subject image must have been only an exponentiation of 2. If it was
not an exponentiation of 2, the Wavelet transform should have been done
after it had been extended to exponentiation of 2.
FIG. 3a and 3b describe extension processing of the prior Wavelet
transform. In the prior Wavelet transform, only predetermined sized
original image could be transformed. In case the size was 137.times.180 as
shown in FIG. 3a, it was enlarged to the size 2.sup.8 .times.2.sup.8
=256.times.256 as shown in FIG. 3b and was transformed, using the extended
image with zero value assigned to the enlarged area.
The multiple resolution analysis of a Wavelet transform is conducted as
follows; Firstly, take out one line of x direction, then let brightness of
the kth of the 256 pixels Ck.sup.(0). The value in the bracket of
Ck.sup.(0) describes the transforming level. One octave down makes the
value -1.
Next, following the resolving algorithm, obtain 128 low resolution
components Cn.sup.(-1) and 128 Wavelet components dn.sup.(-1) using the
following (expression 1) and (expression 2).
c.sub.n.sup.(-1) =(1/2).SIGMA..sub.k p.sub.k-n c.sub.k.sup.(0)(expression
1)
d.sub.n.sup.(-1) =(1/2).SIGMA..sub.k q.sub.k-2n c.sub.k.sup.(0)(expression
2)
.SIGMA..sub.k indicates the sum total from k=0 to 255. Also, p.sub.k and
q.sub.k are coefficients of two scale functions; a scaling function
.phi.(x) and a Wavelet function .psi.(x), respectively.
.phi.(x)=.SIGMA.p.sub.k .phi.(2x-k) (expression 3)
.psi.(x)=.SIGMA.q.sub.k .phi.(2x-k) (expression 4)
However, .SIGMA. indicates the sum total from k=0 to m (support length of a
function: length of the area which function value is not zero.)
After finishing the above resolution to all the x direction lines, conduct
the same to all the y direction rows as well. As a result, the low
resolution components will be gathered in the 128.times.128 area.
Next, again, conduct the same to the 128.times.128 area to get low
resolution component of 64.times.64. Repeat this until it gets the
predetermined resolution. Normally around 4 times would be enough.
Generally, in compression using transforming, the higher the
compressibility ratio is, the lower the quality of the restored image. In
case of JPEG, it has guaranteed the quality of image with establishing
"Quality Parameter".
This method, however, is not accurate since it reduces the data by
adjusting the divided value with an integer. In this case, the
signal-to-noise ratio was calculated after output of the restored image,
compared with the original image.
As stated above, the image compression by a Wavelet transform for any sized
image has not been studied till now in spite of its necessity as a
practical matter. Processing process must be simple with the method of
assigning zero value to the extended area by extending the image frame
like existing JPEG system. However, the computing time and the amount of
memory needed will be increased with the increasing amount of the assigned
zero. If things come to the worst, four times of the amount of original
memory would be needed.
Also, it took a long time to check the restored image quality since it had
to compare the original image and restored image after restoring the
image.
SUMMARY OF THE INVENTION
The main purpose of this invention is to create an apparatus which
efficiently compresses and restores images which makes it possible to
minimize zero area mentioned above to reduce the computing time and the
amount of memory needed.
Also, another purpose of this invention is to create an apparatus which is
able to estimate the signal-to-noise ratio when the data is reduced.
To attain the above objects, according to one aspect of the present
invention, there is provided an image compressing apparatus having a
Wavelet transforming unit for compressing digitized image data using a
Wavelet transform, said Wavelet transforming unit comprising:
a means which extends image data area to make the number of data of the
subject of transforming of horizontal and vertical directions even, with
every one octave of resolution down when a Wavelet transform is conducted
hierarchically based on multiple resolution analysis and another means
which interpolates values in extended image data area using data in image
data area before extension to conduct a Wavelet transform on data of that
interpolated image data area.
Also, according to another aspect of the present invention, there is
provided an image restoring apparatus having an inverse Wavelet
transforming unit for restoring image data compressed by a Wavelet
transform, said inverse Wavelet transforming unit comprising a means which
reduces redundancy generated by extension of image data area caused by
image data compression when the image data is restored with every one
octave of resolution up.
Also, according to still another aspect of the present invention, there is
provided an apparatus for transforming image data using a Wavelet
transform, comprising an image compressing apparatus having a Wavelet
transforming unit for compressing digitized image data and an image
restoring apparatus having an inverse Wavelet transforming unit for
restoring image data compressed by said image compressing apparatus, said
Wavelet transforming unit in the image compressing apparatus comprising a
means which extends image data area to make the number of transforming
subject data of horizontal and vertical directions even, with every one
octave of resolution down when a Wavelet transform is conducted
hierarchically based on multiple resolution analysis to conduct a Wavelet
transform on data of that interpolated image data area and the Wavelet
transforming unit mentioned above in the image restoring apparatus also
mentioned above have a means which reduces redundancy generated by
extension of image data area caused by image data compression when the
image data is restored with every one octave of resolution up.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects and features of the present invention will be described
hereinafter in detail by way of preferred embodiments with reference to
the accompanying drawings, in which;
FIG. 1a-FIG. 1c describe the compressing process using the Wavelet
transform;
FIG. 2 shows one example of the restored data generated by a Wavelet
transform;
FIG. 3a and FIG. 3b describe the extending process of the prior Wavelet
transform technology;
FIG. 4 is a block diagram which shows the principal structure of the image
data transforming apparatus using a Wavelet transform on this invention;
FIG. 5 is a block diagram which shows one example of the structure of
Wavelet image compressing apparatus described in FIG. 4;
FIG. 6 shows one example of a Wavelet function;
FIG. 7a-FIG. 7j describe a Wavelet transform, following the first
embodiment of this invention;
FIG. 8 is a flowchart which shows a Wavelet transform, following the first
embodiment of this invention;
FIG. 9a-FIG. 9d describe a Wavelet transform, following the second
embodiment of this invention;
FIG. 10a and FIG. 10b show one example of numbering processing;
FIG. 11 is a flowchart which shows one example of the data reducing
process;
FIG. 12 is a block diagram which shows one example of the structure of
Wavelet image compression apparatus described in FIG. 4;
FIG. 13a-FIG. 13f describes a Wavelet image transforming process of prior
technology (zero assigning method);
FIG. 14a-FIG. 14m describe a Wavelet image transforming process, following
the first embodiment of this invention;
FIG. 15a-FIG. 15f describe the Wavelet image transforming process,
following the second embodiment of this invention;
FIG. 16 shows the time required for computation and the compressibility
ratio based on each embodiment of this invention compared with the prior
art (zero assigning method).
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 4 describes the principal of this invention.
The Wavelet image compressing apparatus 1 is consisted of the Wavelet
transforming unit 11 which includes the size adjusting unit 12, the
numbering processing unit 13, the data reduction processing unit 14 and
the entropy coding unit 15. The Wavelet image compressing apparatus 2 is
consisted of the entropy decoding unit 21, the numbering restoration
processing unit 22, the inverse Wavelet transforming unit 23, having the
inverse size adjusting unit 24 and the restored image display processing
unit 25.
The original image data 3 is an image data to be the subject of
compression. The input parameter 4 is a parameter used for image
compressing control of the original image size, the function
discrimination number used for a Wavelet transform and image quality
threshold values. The compressed data 5 is data which is consisted of
image data compressed by the Wavelet image compressing apparatus 1 and
values required for the restoration.
The Wavelet transforming unit 11 conducts a Wavelet transform
hierarchically based on the multiple resolution analysis.
The size adjusting unit 12 adjusts size of the original image data 3 to the
suitable size for a Wavelet transform. In case there are many hierarchies
in the multiple resolution analysis or the number of hierarchy is not
fixed, for example, the size adjusting unit 12 checks the number of data
of the subject of transforming whether it is an odd or even number, with
every one octave of the resolution down. If the number is odd, it extends
the image data area to make it even number and interpolates the value of
extended image data area with data of the image data area before the
extension.
Or, in case the number of hierarchy in the multiple resolution analysis is
small or that number is fixed in advance, it extends the image data area
to make the number of data of the subject of transforming even, only for
the number of the hierarchy. Then it interpolates the value of extended
image data area with data of the image data area before the extension.
The Wavelet transforming unit 11 conducts a Wavelet transform for the data
in the image data area extended and interpolated as above.
The numbering processing unit 13 is a unit which assigns numbers to the
resolution; the lower the resolution is, the smaller the number is. The
data reduction processing unit 14 is a unit which sorts the transformed
values according to descending order of amplitude value and reduces data
sequentially in ascending order of amplitude value, estimating the quality
of restored image quantitatively. The entropy coding unit 15 is a unit
which compresses data by entropy coding and generates the compressed data
5.
The entropy decoding unit 21 of the Wavelet image restoring apparatus 2 is
a unit which entropy decodes the compressed data 5 using inverse
transforming of coding process of the entropy coding unit 15. The
numbering restoration processing unit 22 is a unit which reassign numbers
given by the numbering processing unit 13 to data which restored by the
entropy decoding unit 21 and restores the original list.
The inverse Wavelet transforming unit 23 is a unit which generates restored
data using inverse transforming of transforming process at the Wavelet
transforming unit 11.
The inverse size adjusting unit 24 conducts process which omits redundancy
generated by extending process of the size adjusting unit 12 with every
one octave up by the inverse Wavelet transforming unit 23. Or, it conducts
process which omits redundancy generated by extending process of the size
adjusting unit 12 when multiple resolution analysis by the inverse Wavelet
transforming unit 23 is terminated.
The restored image display processing unit 25 is a unit which displays
images based on restored data obtained from the inverse Wavelet
transforming unit 23.
The Wavelet image compressing apparatus 1 takes optional sized original
image data 3, adjusts the original image size to suitable size for
transforming, following provided input parameter 4 to conduct a Wavelet
transform and generates the compressed data 5 through numbering process,
data reducing process and entropy coding. The Wavelet image restoring
apparatus 2 conducts entropy decoding and numbering restoring process from
the compressed data 5 when required, omits redundancy which is the area
extended by size adjustment at compressing process and obtains the
restored image through the inverse Wavelet transforming process.
Consequently, it is possible to transform any provided sized image to the
compressed data all at once and restore them to obtain the restored image
when required. Also, the smaller the extended size is, the smaller the
amount of computation time and the memory needed, which makes it possible
to conduct efficient transforming by size adjustment. Furthermore, the
compressibility ratio will be improved with the smaller data distribution.
The data reduction processing unit 14 reduces data from the one with
smaller amplitude within the range that the signal-to-noise ratio is not
exceeded the threshold value. Here the data is almost listed in the
ascending order of amplitude values by the numbering processing unit 13 to
improve the compressibility ratio with the reduced data with smaller
numbers.
Embodiments of this invention will be described hereinafter with the
figures.
FIG. 5 shows a structure example of the Wavelet image compressing
apparatus.
The multiple resolution analyzing unit 32 in the Wavelet transforming unit
31 conducts multiple resolution analysis, using the image size 41 and the
function discrimination number obtained by the input parameter 4. As for a
Wavelet function, normal orthogonal function is desirable rather than
biorthogonal function. FIG. 6 shows some examples of usable functions.
These functions are determined to indicate p.sub.k and q.sub.k value in
FIG. 6 on the said expressions (expression 1 and 2). There are three
functions and each one of them can be used.
The size adjusting unit 33 adjusts size of the original image data 3 to
suitable image size for a Wavelet transform. There are two ways for the
size adjusting process. The first adjusting method and the second
adjustment method are described as the first embodiment and the second
embodiment, respectively as follows;
The First Embodiment
The first embodiment is an effective way in case the number of hierarchy in
the multiple resolution analysis is large or the number of hierarchy is
not determined. With the first embodiment, the area size of image data of
the subject of transforming will be extended to make it even number and
the size adjusting process will be conducted to interpolate the extended
data points. In other words, when the number of data (pixels) of one side
of data which will be conducted resolution analysis is odd, data points
will be extended only one row or line to be interpolated to be assigned
average values at both ends of original row of data.
FIG. 7a-FIG. 7j describe the Wavelet transforming process using the first
embodiment.
As shown in FIG. 7a, if an original image of the subject of transforming is
137.times.180 size, the number of data of x direction is odd. In this
case, data point will be extended one row and the average data value of
the first and the 137th row from the left will be assigned to the 138th
line which is the extended one. Since the number of data of y direction
here is even, extension will not be needed. Then resolution analysis will
be conducted to x direction followed by another resolution analyzing to y
direction conducted on that result. The area L.sub.0a where the low
resolution components are concentrated and the Wavelet components will be
obtained.
FIG. 7c shows condition after the first resolution analyzing. L.sub.0a is
an area where the low resolution components of x and y direction are
concentrated, H.sub.0b is an area of the high resolution component with x
direction and the low resolution component with y direction, H.sub.0c is
an area of the low resolution component with x direction and the high
resolution component with y direction, and H.sub.0d is an area where the
high resolution components of x and y direction are concentrated.
Next, the second resolution analyzing will be conducted on the area
L.sub.0a. Since the number of data to x direction is odd, data point will
be extended again one row as shown in FIG. 7b. That extended data row will
be shifted the 70th lateral row in the L.sub.0a area to be interpolated.
In other words, average value of the first and 69th line values will be
assigned to the shifted 70th row.
FIG. 7e shows an image data area after shifting and interpolating. The
L.sub.0a area size becomes 70.times.90 at this time and another Wavelet
transform will be conducted on this L.sub.0a area. The transformed data
areas will be L.sub.1a, H.sub.1b, H.sub.1c, H.sub.1d (cf. FIG. 7f).
Then the area L.sub.1a will be transformed. Since the L.sub.1a area size is
35.times.45 and the number of data to both x and y directions is odd, data
point will be extended one line to y direction as shown in FIG. 7g. Also
data point will be extend one row to x direction. Then the extended data
line and row will be shifted to interpolate the value. With it, the
L.sub.1a area will be 36.times.46 size, which makes it possible to be
transformed again.
FIG. 8 shows a flowchart of the Wavelet transforming process on the first
embodiment.
Step S1 judges the number of data of x direction whether it is odd or not.
If the number of data is odd, go to Step S2 to be processed, or in case
the number is even, go to Step 3.
Step S2 extends the size and interpolates it by adding average values at
both ends to the end of row of data.
Step S3 analyzes resolution of x direction.
Step S4 judges the number of data of y direction whether it is odd or not.
If the number of data is odd, go to Step S5 to be processed, or in case
the number is even, go to Step 6.
Step S5 extends the size and interpolates by adding average values at both
ends to the end of row of data.
Step S6 analyzes resolution of x direction.
Step S7 judges the resolution whether it is a predetermined one or not. If
it is, the process will be terminated. If it is not, go back to Step S1 to
repeat analyzing resolution in the same way.
The Second Embodiment
The second embodiment is an effective way in case the number of hierarchy
in the multiple resolution analysis is small. With the second embodiment,
the size of original image data 3 will be extended to make only the
predetermined number of hierarchy even number and the size adjusting
process will be conducted to interpolate the extended data points. In
other words, when the number of data point of one side of the original
image data 3 is a, and b hierarchies (the number of hierarchy) will be
transformed, It finds the minimum value within x which makes x/2.sup.b
integer (x.gtoreq.a) to extend and interpolate the image area to make it x
line or x row in advance.
FIG. 9a-FIG. 9b describe the Wavelet transforming process using the second
embodiment.
As shown in FIG. 9a, an original image of the subject of transforming is
137.times.180 size and determined to analyze resolution up to 4 octaves.
In other words, analyze resolution 4 times. In this case, find the minimum
value which makes the size of x and y directions even, with the 4 times
process. In this example, the x direction should be 144 and the y
direction should be 192, since 144.div.2.sup.4 =9 (integer) and
192.div.2.sup.4 =12 (integer).
Consequently, 7 rows data points to the x direction and 12 lines data
points to the y direction will be extended to interpolate data in the
extended area. The interpolation will be conducted by assigning values
from both ends of the image to the extended area. Then the extended and
interpolated area will be transformed. FIG. 9c shows condition after the
first resolution analyzing. As described in FIG. 7a-FIG. 7j, the areas
will be L.sub.0a, H.sub.0b, H.sub.0c, H.sub.0d.
FIG. 9d shows area after the second resolution analyzing. The third
resolution analyzing will be conducted to the L.sub.1a area, followed by
the 4th resolution analyzing to L.sub.2a area generated by the third
resolution analysis.
For the data obtained by a Wavelet transform described as the first or the
second embodiment as above, data compression will be conducted as follows.
The numbering processing unit 34 assigns numbers; the lower the resolution
of transformed value, the smaller the number is. This process assigns
numbers for changing order of data to reduce and compress data
efficiently. The numbering method may be, for example, assigning numbers
to lines and rows reciprocally as shown in FIG. 10a, or assigning numbers
by scanning to the direction of lines or rows from the lower resolution
area as shown in FIG. 10b.
The amplitude value sorting unit 37 in the data reduction processing unit
35 sorts transformed values obtained by the Wavelet transforming unit 31
according to descending order of amplitude vale. This is a preparation for
reducing data in ascending order of amplitude value and it is sorted as a
set of assigned number before the sorting and the transformed value.
The data reducing unit 36 reduces data in ascending order of amplitude
value. At that time, it reduces within a range which keeps a certain image
quality, estimating the restored image by the transformed value sorted by
the amplitude vale sorting unit 37, using the image quality threshold
value.
If a normal orthogonal function is used as a Wavelet function, calculate
the sum of a square of the amplitude value of data which will be reduced
and if that value exceeds a certain value, terminate the data reduction.
FIG. 11 is a flowchart of the data reducing process.
Step S11 sorts transformed values according to descending order of
amplitude value.
Step S12 initializes a integrated value X to zero.
Step S13 makes transformed value whose amplitude value is not zero and
which has the smallest value "Y" and make its number "I".
Step S14 conducts X=X+Y.sup.2 which integrates the sum of a square of the
amplitude value of data which will be reduced.
Step S15 judges whether X exceeds a certain threshold value or not. If X is
more than the threshold value, it terminates the data reduction and if X
is less than the threshold value, it conducts Step S16 process.
Step S16 reduces data, making i-th transformed value zero. Then go back to
Step 513 to repeat the process until X will exceed the threshold value.
Threshold value used in Step S15 will be determined by the principle as
follows;
Firstly, signal-to-noise ratio of restored image can be obtained from the
integrated value X of a square of amplitude value with an expression
(expression 5) as follows;
10 log.sup.10 (ND.sup.2 /X) (expression 5)
The unit here is dB (decibel), N is the number of pixel and D is the number
of gradient of brightness. The quality of image will be guaranteed unless
this value is less than a certain value Z.
As for Z value, 30 dB is generally selected. When it is actually
calculated, for reducing the number of operation times, (expression 6)
which counts backward from (expression 5) will be used as follows;
X>ND.sup.2 10.sup.-Z/10 (expression 6)
If this right side is calculated only once, data reduction can be conducted
within a range which satisfies the (expression 6). Therefore, the right
side of this (expression 6) is used as a threshold value of Step S15.
Also, Z can be provided from outside as the image quality threshold value
43 of the input parameter 4.
Effects of extending and interpolating image area is too small to consider,
however, when it is taken into account, the sum of a square of data
interpolated from integrated value X should be deducted in advance.
The entropy coding unit 38 encodes reduced data. As for the entropy coding
method, any of the coding as Huffman coding, arithmetic coding or LZW
method can be used. Those coding methods are well known and each detail
will be omitted.
When the compressed data 5 is retained, the original data size and the kind
of used Wavelet function should be also retained with the image data
itself.
FIG. 12 shows one structure example of the Wavelet image restoring
apparatus.
To generate restored image from the compressed data 5, conduct the process
described with the structure example of the Wavelet image compressing
apparatus in FIG. 4 in totally inverse order. The compressed data 5 will
be transformed in inverse order of entropy coding by the entropy decoding
unit 51. The numbering restoration processing unit 52 assigns numbers by
inverse order of the numbering process shown in FIG. 10a and FIG. 10b for
data restored by the entropy decoding unit 51 to restore the listing
order.
The inverse Wavelet transforming unit 53 conducts inverse transforming of
that of the Wavelet transforming unit 31 in FIG. 5, using the multiple
resolution analyzing unit to restore images. On this occasion, it omits
the redundant part extended by the size adjusting unit 33 in FIG. 5, using
the inverse size adjusting unit 55 with every hierarchy or when all the
multiple resolution analyzing is terminated. It also displays the restored
image on display apparatus using the restored image display processing
unit 56 when required.
A expression used for inverse transformation in the inverse Wavelet
transforming unit 53 is (expression 7) as follows;
c.sub.k.sup.(0) =.SIGMA..sub.n p.sub.k-2n c.sub.n.sup.(-1) +q.sub.k-2n
d.sub.n.sup.(-1) (expression 7)
.SIGMA..sub.n shows the sum total from n=0 to N (N is the number of pixels
in one side). Also, p.sub.k and q.sub.k are coefficients of two scale
function of a scaling function .phi.(x) and a Wavelet function .psi.(x),
respectively (cf. expression 3 and expression 4).
Next, the first embodiment of the case which extends/interpolates an
original image of 5.times.6 pixels with every multiple resolution analysis
(the first embodiment) and the second embodiment of the case which
extends/interpolates at a time when 3-octave resolution analyzing is
conducted to an original image of 5.times.6 pixels (the second embodiment)
will be described.
Wavelet transform using "Daubechies N=22", which is one of the functions
shown in FIG. 6, as a Wavelet function was conducted. As for data
reduction processing, it was set that the restored image was about 30 dB.
As for entropy coding method, "LZ 77" was used.
Firstly, to clarify the difference between this invention's embodiments and
the prior art, the process of compressing and restoring image data by zero
assigning method which is the prior art will be described here.
FIG. 13a-FIG. 13f describe the prior art (zero assigning method).
As shown in FIG. 13a, if an original image of the subject of process is
5.times.6 pixels, extend the area to 8.times.8 pixels to make one side
length an exponentiation of 2.
Then, conduct transforming process (cf. FIG. 13c) and data reducing process
(cf. FIG. 13d) to generate the compressed data. If this compressed data is
restored by inverse Wavelet transforming, 8.times.8 sized image data will
be obtained as shown in FIG. 13e. Assign zero and omit generated extension
area to obtain the restored image with the original image size, 5.times.6.
FIG. 13f shows the restored image with the original image size.
Next, the first embodiment which extends/interpolates with every multiple
resolution analysis (MRA) will be described, using FIG. 14a-FIG. 14m.
FIG. 14a shows an original image of 5.times.6 pixels. Since the number of
pixel in x direction is odd, extension and interpolation to x direction
will be conducted as shown in FIG. 14b. For example, the interpolated
value "106", which is at the right end of the first line, is the average
of the original values which are at the both ends of the first line, "89"
and "123".
Since the number of pixel in y direction is even, extension will not be
conducted. The number of pixel of the subject of transforming will be
6.times.6 by this extension. Multiple resolution analysis (MRA) to x
direction will be conducted on it. Then, multiple resolution analysis to y
direction will be conducted as shown in FIG. 14d.
Since the low resolution component area in FIG. 14d is 3.times.3, extend
the lines and rows as shown in FIG. 14e and shift the extended zero area
to the center to continue more multiple resolution analysis.
Then, interpolate the value of rows extended to x direction as shown in
FIG. 14f to conduct multiple resolution analysis to x direction. The
result will be shown as in FIG. 14g.
Then, interpolate also for y direction using shifted zero area to conduct
multiple resolution analyzing as shown in FIG. 14b. Then repeat multiple
resolution analysis to both x and y directions. FIG. 14k shows data after
above transforming processes.
After that, data reduction will be conducted, estimating quality of image
of the restored image quantitatively. FIG. 14l shows data after reduction
processing. After data reduction processing, entropy coding will be
conducted to generate the compressed data.
The restored data will be generated through a series of compressing process
and inverse restoring process from the compressed data. FIG. 14m shows
restored data (5.times.6 pixels) generated by restoring process of the
compressed data shown in FIG. 14l.
Next, the second embodiment which conducts extension/interpolation of
necessary amount at a time in the beginning, when 3-octave resolution
analyzing will be conducted to an original image of 5.times.6 pixels.
FIG. 15a shows an original image of 5.times.6 pixels. Since the minimum
size of image data which makes the number of pixel to be transformed by
3-octave resolution analyzing always even is 8.times.8, extend area for 3
pixels to x direction and 2 pixels to y direction. FIG. 15b shows an image
data after the extension. The one side length in this example is an
exponentiation of 2, however, it is not always an exponentiation of 2.
Then, interpolate the extended area as shown in FIG. 15c. An interpolated
value is determined based on values at both ends of the same line or row.
For example, interpolated values in the first line "115, 106, 98" are
determined to be the average of the values at both ends of the original
line. Multiple resolution analysis will be conducted on this interpolated
8.times.8 sized image data. FIG. 15d shows the image data after transform
processing.
The data after reduction processing is shown in FIG. 15e. The compressed
data will be generated on this by entropy coding.
The image will be restored based on this compressed data by the Wavelet
image restoring apparatus 2. FIG. 15f shows the restored data generated by
restoration processing (5.times.6 pixels).
FIG. 16 shows comparison of the time required for computation and
compressibility ratio of the prior art (zero assigning method), the first
embodiment and the second embodiment.
In "read" time, as for compression processing, it comprises the operation
time for file reading and creating numbering corresponding table. As for
restoration processing, it comprises the operation time for file reading,
creating numbering corresponding table and entropy decoding. In "WT" time,
as for compression processing, it is time for the Wavelet transform and as
for restoration processing, it is the time for the inverse Wavelet
transform. In "write" time, as for compression processing, it comprises
the operation time for data reduction processing, entropy coding and file
output. As for restoration processing, it is the time for the restored
image data output.
As shown in FIG. 16, this invention has improved the time required for
computation and the compressed file size 0.4 times and 0.5 times,
respectively. The reason of the computation Lime reduction is because the
necessary array is minimized. The reason of the compressibility ratio
improvement is because the data distribution range is reduced by
interpolation of the extended area.
When the results of first embodiment and the second embodiment are
compared, the time required for computation is almost the same, however,
the file size of the second embodiment is slightly larger than that of the
first embodiment. The reason of this is because in the second embodiment,
interpolation is conducted even if one side of the image data is even to
make the range of data distribution of the transformed value smaller.
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